As elevators operate in a group serving a common set of floors, the cars frequently will be close together with respect to position and direction. For instance, in a four-car group, it is not uncommon to observe three elevators traveling up in the lower portion of the building. This phenomenon is called "bunching." Bunching is defined loosely to mean that certain cars are "close together". The absence of bunching means that the cars are evenly distributed amongst the floors. Bunching is not always undesirable, as when several cars converge to a convention floor to move a large number of people. As a rule, however, bunching is undesirable. In general, a system in which the cars are evenly distributed amongst the floors will result in a minimum average waiting time for the randomly arriving passenger.
The phenomenon of bunching is illustrated in FIG. 1 which shows both Cars A and B traveling down in the top part of a 15-story building. Also, Cars C and D are reasonably close to one another. A wait-so-far time, when the hall call was registered to the present time, is shown for each hall call. The waiting time is the time from when a passenger presses a hall call button until the elevator arrives. Intuitively, a longer than desired waiting time might occur if a passenger would register a down hall call at Floor 15. The maximum waiting times could be reduced if the cars were more evenly distributed: Car A might be positioned at Floor 7-DOWN, and Car C might be positioned at floor 8-UP. With reference to FIG. 1, it can be seen that this repositioning of the cars is impossible because of the hall call and car call assignments. The impossibility of the proposed repositioning of the cars underscores the difficult nature of solving the bunching problem.